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A204847 Primitive cofactor of n-th repunit A002275(n). 4
1, 11, 111, 101, 11111, 91, 1111111, 10001, 333667, 9091, 11111111111, 9901, 1111111111111, 909091, 90090991, 100000001, 11111111111111111, 999001, 1111111111111111111, 99009901, 900900990991, 826446281, 11111111111111111111111, 99990001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Except for a(1) = 1 and a(3) = 111, this is the Zsigmondy numbers for a = 10, b = 1: Zs(n, 10, 1) is the greatest divisor of 10^n - 1^n that is coprime to 10^m - 1^m for all positive integers m < n. The prime terms are called unique primes or unique period primes (A007615).

Differs from A019328 for n = 1, 9, 22, 27, 42, ... - Jianing Song, Apr 30 2018

LINKS

Table of n, a(n) for n=1..24.

Makoto Kamada, Factorizations of 11...11 (Repunit).

Samuel Yates, Cofactors of repunits, Journal of Recreational Mathematics, Vol. 8(2), pp. 99, 1975-76.

Samuel Yates, The Mystique of Repunits, Math. Mag. 51 (1978), 22-28.

FORMULA

Equals A002275(n)/(product of terms in n-th row of A204845).

PROG

(PARI) lista(nn) = {vf = []; vfs = []; for (n=1, nn, if (n==1, print1(n, ", "), f = factor((10^n-1)/9)[, 1]; vkeep = []; for (k = 1, #f~, if (!vecsearch(vfs, f[k]), vkeep = concat(vkeep, f[k])); ); print1(prod(j=1, #vkeep, vkeep[j]), ", "); vf = concat(vf, vkeep); vfs = Set(vf); ); ); } \\ Michel Marcus, May 18 2018

CROSSREFS

Cf. A002275, A019328, A102380, A204845, A204846.

Sequence in context: A061493 A093788 A327992 * A098759 A273977 A135464

Adjacent sequences:  A204844 A204845 A204846 * A204848 A204849 A204850

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Jan 19 2012

EXTENSIONS

a(11)-a(24) from Jianing Song, Apr 30 2018

STATUS

approved

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Last modified April 18 02:38 EDT 2021. Contains 343072 sequences. (Running on oeis4.)